title: Analysis of partial and complete protection in malaria cohort studies.
abstract: BACKGROUND
  Malaria transmission is highly heterogeneous and analysis of incidence data must account for this for correct statistical inference. Less widely appreciated is the occurrence of a large number of zero counts (children without a malaria episode) in malaria cohort studies. Zero-inflated regression methods provide one means of addressing this issue, and also allow risk factors providing complete and partial protection to be disentangled.
  
  
  METHODS
  Poisson, negative binomial (NB), zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) regression models were fitted to data from two cohort studies of malaria in children in Ghana. Multivariate models were used to understand risk factors for elevated incidence of malaria and for remaining malaria-free, and to estimate the fraction of the population not at risk of malaria.
  
  
  RESULTS
  ZINB models, which account for both heterogeneity in individual risk and an unexposed sub-group within the population, provided the best fit to data in both cohorts. These approaches gave additional insight into the mechanism of factors influencing the incidence of malaria compared to simpler approaches, such as NB regression. For example, compared to urban areas, rural residence was found to both increase the incidence rate of malaria among exposed children, and increase the probability of being exposed. In Navrongo, 34% of urban residents were estimated to be at no risk, compared to 3% of rural residents. In Kintampo, 47% of urban residents and 13% of rural residents were estimated to be at no risk.
  
  
  CONCLUSIONS
  These results illustrate the utility of zero-inflated regression methods for analysis of malaria cohort data that include a large number of zero counts. Specifically, these results suggest that interventions that reach mainly urban residents will have limited overall impact, since some urban residents are essentially at no risk, even in areas of high endemicity, such as in Ghana.
authors.affiliation: MRC Tropical Epidemiology Group, London School of Hygiene & Tropical Medicine, London, UK. matthew.cairns@lshtm.ac.uk.
authors.forename: Matthew E
authors.initials: ME
authors.lastname: Cairns
authors.forename: Kwaku Poku
authors.initials: KP
authors.lastname: Asante
authors.forename: Seth
authors.initials: S
authors.lastname: Owusu-Agyei
authors.forename: Daniel
authors.initials: D
authors.lastname: Chandramohan
authors.forename: Brian M
authors.initials: BM
authors.lastname: Greenwood
authors.forename: Paul J
authors.initials: PJ
authors.lastname: Milligan
mesh_terms: D002675:Child, Preschool; D015331:Cohort Studies; D004812:Epidemiologic Methods; D005260:Female; D005869:Ghana / Q000453:epidemiology; D006801:Humans; D015994:Incidence; D007223:Infant; D007231:Infant, Newborn; D008288:Malaria / Q000453:epidemiology*; D008297:Male; D012307:Risk Factors; D013223:Statistics as Topic